AUROC

AUROC stands for area under the receiver operating characteristic curve, a metric for evaluating binary classifiers. The ROC curve plots the true positive rate (sensitivity) against the false positive rate (1 − specificity) across different decision thresholds, describing how a model's ability to discriminate between positive and negative classes changes with threshold.

The AUROC is the area under that curve and yields a value between 0 and 1. A value of 0.5 indicates no discriminative ability beyond random chance, while 1.0 indicates perfect discrimination. In probabilistic terms, the AUROC equals the probability that a randomly chosen positive instance is ranked higher by the model than a randomly chosen negative one.

Calculations typically use the trapezoidal rule to integrate the ROC curve points. AUROC is equivalent to the probability that a randomly selected positive is ranked above a randomly selected negative; related to the Mann–Whitney U statistic. In survival analysis, time-dependent AUROC assesses discrimination over time, and partial AUROC focuses on a specified range of FPR or TPR.

AUROC has limitations. It is insensitive to class distribution but can be misleading on highly imbalanced data; precision–recall curves (AUPRC) may be more informative in such cases. It does not measure calibration, i.e., whether predicted probabilities reflect true frequencies. Statistical comparisons use methods such as DeLong's test or bootstrap confidence intervals; model calibration and clinical relevance should also be considered.

AUROC is widely used in medicine, bioinformatics, and machine learning to compare diagnostic tests, risk scores, and classifiers. It provides a single-summary measure of discrimination, complementing other evaluation metrics that reflect calibration and clinical consequences.